Field-Programmable Gate Arrays (FPGAs) are increasingly shaping the future of network security, thanks to their flexibility, parallel processing capabilities, and energy efficiency. In this survey, we examine 50 peer-reviewed studies published between 2020 and 2025, selected from an initial pool of 210 articles based on relevance, hardware implementation, and the presence of empirical performance data. These studies encompass a broad range of topics, including cryptographic acceleration, intrusion detection and prevention systems (IDS/IPS), hardware firewalls, and emerging strategies that incorporate artificial intelligence (AI) and post-quantum cryptography (PQC). Our review focuses on five major application areas: cryptographic acceleration, intrusion detection and prevention systems (IDS/IPS), hardware firewalls, and emerging strategies involving artificial intelligence (AI) and post-quantum cryptography (PQC). We propose a structured taxonomy that organises the field by technical domain and challenge, and compare solutions in terms of scalability, resource usage, and real-world performance. Beyond summarising current advances, we explore ongoing limitations—such as hardware constraints, integration complexity, and the lack of standard benchmarking. We also outline future research directions, including low-power cryptographic designs, FPGA–AI collaboration for detecting zero-day attacks, and efficient PQC implementations. This survey aims to offer both a clear overview of recent progress and a valuable roadmap for researchers and engineers working toward secure, high-performance FPGA-based systems.